If the run is too small that it would not be humane to keep them in there 24/7, it needs to be expanded. Period.
If it's not reasonable to put fencing because of how the property lines work, I'm not sure you have a lot for options. As someone else already mentioned, you could try to figure out what it is about the neighbor's place that has them going over there, but even if you put those things on your property it's no guarantee your chickens are going to stay. I'm glad you're asking about this though, as it is 100% your responsibility to keep your animals off your neighbors property.
I had a problem with chickens going into the woods behind their hen house and a couple of them got grabbed by predators a couple years ago. I put fencing just along that portion behind their coop and they don't go in the woods over there anymore, even though there are a lot of other entry points. Maybe fencing in a few strategic places would be enough to deter them.